Scilab Function
Last update : Dec 1997

cdfgam - cumulative distribution function gamma distribution

### Calling Sequence

  `[P,Q]=cdfgam("PQ",X,Shape,Scale)`
  `[X]=cdfgam("X",Shape,Scale,P,Q)`
  `[Shape]=cdfgam("Shape",Scale,P,Q,X)`
  `[Scale]=cdfgam("Scale",P,Q,X,Shape)`

### Parameters

- `P,Q,X,Shape,Scale`: five real vectors of the same size.
- `P,Q (Q=1-P)` The integral from 0 to X of the gamma density. Input range: [0,1].
- `X`: The upper limit of integration of the gamma density. Input range: [0, +infinity). Search range: [0,1E300]
- `Shape`: The shape parameter of the gamma density. Input range: (0, +infinity). Search range: [1E-300,1E300]
- `Scale`: The scale parameter of the gamma density. Input range: (0, +infinity). Search range: (1E-300,1E300]

### Description

Calculates any one parameter of the gamma distribution given values for the others.

Cumulative distribution function (P) is calculated directly by the code associated with:

DiDinato, A. R. and Morris, A. H. Computation of the incomplete gamma function ratios and their inverse. ACM Trans. Math. Softw. 12 (1986), 377-393.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

The gamma density is proportional to `T**(SHAPE - 1) * EXP(- SCALE * T)`

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.